I discovererd this in a Patricia Wells book several years ago and have really enjoyed it in late summer when there are so many wonderful ripe tomatoes in abundance and loooking for one more thing to do with them.
Take 2 lbs, firm ripe tomatoes and peel and core them. Cut them into quarters length wise. Place on paper towels and sprinkle lightly with salt and cover with another paper towel and drain them for an hour (sometimes I do not bother peeling).
Combine 2 lg. eggs, 2 yolks from lg. eggs, 1/3 C. heavy cream, 1/4 C. freshly grated Parmesan cheese and a tsp.of fresh thyme or minced basil. Blend well.
Layer the tomatoes in a baking dish and pour the batter over them and sprinkle on another 1/4 C. freshly grated Parmesan cheese and another tsp. of fresh thyme leaves or minced basil.
Bake at 375 F in the center of the oven until the batter is set and the clafout is golden. Serve warm